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Abstract

We measure the normal-incidence transmission coefficient of photonic crystal slabs with hexagonal arrays of air holes in silicon. The transmission spectra exhibit sharp resonant features with Fano line shapes. They are produced due to the coupling of the leaky photonic crystal modes, called guided resonances, to the continuum of free-space modes. We investigate the effects of several types of structural disorder on the spectra of these resonances. Our results indicate that guided resonances are very tolerant to disorder in the hole diameter and to interface roughness, but very sensitive to disorder in the lattice periodicity.

Figures (9)

A schematic of the experimental setup. The terahertz radiation propagates in the direction perpendicular to the plane of the photonic crystal slab. The terahertz beam spot size is roughly 8 mm. The samples are all very thin compared to the Rayleigh range of the focused THz beam.

(a). A top view of the photonic crystal slab. The scale bar is 5 mm. (b) A magnified portion from (a), with a scale bar of 300 µm. The crystal parameters of this sample are r=150 µm, a=400 µm, and t=250 µm. For a hexagonal lattice, the Γ-K direction points along the axis connecting the centers of adjacent (nearest neighbor) holes, while the Γ-M direction points along the axis connecting the centers of next-nearest neighbors.

Normal-incidence transmission spectrum of a photonic crystal slab with r=150 µm, a=400 µm, and t=250 µm. The open black circles are experimental results, while the solid red curve is obtained from simulations based on the finite elements method (FEM).

Distribution of the hole diameter for perfect (top) and imperfect (middle and bottom) samples. The perfect sample has a mean hole diameter of 297 µm, which is close to the design parameter of 300 µm. The three samples have hole diameters with standard deviations of 1 µm, 32.0 µm, and 39.6 µm, from top to bottom. The samples in the lower two images have different slab thicknesses. The bin size of each bar in the histogram is 5 µm. Images show sample regions within a 8 mm circular area, roughly equal to the THz beam spot size. All scale bars are 1.5 mm.

Normal-incidence transmission spectra of photonic crystal slabs with disorder in the hole size. (a) The solid black curve is the transmission spectrum of the ideal crystal with r=150 µm, a=400 µm, and t=250 µm (top picture, Fig. 4), while the dashed red curve is the spectrum of the corresponding imperfect sample (middle picture, Fig. 4). (b) Same as (a) but for a sample with slightly different slab thickness of 275 µm. The corresponding imperfect sample is shown in Fig. 4 (bottom picture).

Normal-incidence transmission spectra of photonic crystal slabs with r=125 µm, a=400 µm, and t=300 µm. The solid black curve is for the sample with perfectly circular holes [shown in Fig. 6(a)], while the dashed red curve is for a sample with slight disorder in the hole shape [shown in Fig. 6(b)].

Top-view images of photonic crystal slabs with disorder in the lattice parameter. The holes have a diameter of 250 µm, and the lattice parameter of the nominally perfect sample is 400 µm. (a) Sample with no disorder in the lattice parameter. The first column shows a sample region within a 7 mm circular area. The second column shows a magnified portion of the image in the first column. The last column shows the pair correlation function (red) computed from the image in the first column. The (black) vertical lines depict the pair correlation function of a perfect lattice of infinite size. (b) Same as (a), but for a sample with slight disorder in the lattice parameter. (c) Same as (b), but with a greater degree of disorder in the lattice parameter. All scale bars in the first column are 1.5 mm, while those in the second column are 300 µm.

Normal-incidence transmission spectra of photonic crystal slabs with r=125 µm, a=400 µm, and t=300 µm. (a) A perfect sample with no disorder in the lattice parameter [shown in Fig. 8(a)]. (b) A sample with slight disorder in the lattice parameter [shown in Fig. 8(b)]. (c) A sample with greater degree of disorder in the lattice parameter [shown in Fig. 8(c)].